I am doing a sales performance analysis of different products and need to compare the weekly average sales of 2 products to see if one is still higher than the other (Sales of product A is higher than that of B in the past and I want to check if that is still the case). I have the data of sales collected by each period (13 periods), by each store that sold our products (3 stores) and by each week (52 weeks).

The problem is that if I choose the sampling is by week, the sample size is only 3 (1 value for each store) and that makes it fail to follow the normality assumption for two samples t-test.

If I choose to sample by period, the sample size is 13. I tested the normality using Anderson-Darling test and obtain the p-value of 0.1 and 0.2 respectively for each product A and B, which are still greater than 0.05 and I think I could continue with the two sample t-test. But I don't know if I can choose samples by period since the question is to compare average weekly sales.

So my questions are:

  1. Could I choose to sample by period instead of by week even though the question is to compare average weekly sales?
  2. Should I choose to implement a non-parametric alternative instead of two samples t-test? Which are the most suitable test for this problem?

Thank you so much in advance for your attention and your help!


1 Answer 1


I don't think you can come up with a meaningful interpretation or conclusion with a comparison of two population means in this scenario. What is more informative is a trend of weekly sales over a long time period rather than a weekly average whereby a current week's data could be just an anomaly.

A trend is more indicative of a change are more useful for forecasting. You could do this as a trendline connecting the weekly data of sales versus time (weeks) or a bar chart with a weekly series of two bars side by side which could include the individual store contributions.

A more sophisticated test isn't necessarily going to tell you anything more about the data and may even cloud the issue. Some unscrupulous people actually misuse it this way.

  • $\begingroup$ Thanks for your insight! But I need to use hypothesis testing since this is an assignment that requires using hypothesis testing to solve. Do you think it is acceptable if I choose the sample by period instead of by week? $\endgroup$
    – Sophil
    Oct 1, 2018 at 8:11
  • $\begingroup$ You've tested both a single week and a longer period without seeing a statistically significant result for either. Use the longer period with the larger sample size and simply fail to reject the null and conclude you have no evidence of a change in sales order of the two products. $\endgroup$
    – Phil H
    Oct 1, 2018 at 13:53
  • $\begingroup$ Sorry Phil! I have somehow missed your latest reply! Thanks so much for your response! $\endgroup$
    – Sophil
    Nov 3, 2018 at 4:56

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